The radius of a circle is changing at the rate of 1/π inches per second. At what rate, in square inches per second, is the circle’s area changing when the radius is 5 inches?

formula for the area A of a circle in terms of its radius r:

   A = πr2

It is important to remember that both r, and hence, A are functions of time, t.  Take the derivative of both sides with respect to t and obtain

   dA/dt = 2πr(dr/dt)

Note that we are using implicit differentiation here, since A and r are (implicit) functions of t.  Now we can find the required answers.

r = 5 inches.

Substitute r = 5 and dr/dt = 3 to get

   dA/dt = 2π5·3 = 30π ≅ 95.25

(the units are in2/min.)

r = 22 inches

   dA/dt = 2π22·3 = 132π ≅ 414.69

Hope that helps.

i'm not entirely sure

step-by-step explanation:

if you ask home depot or lowe's they might be able to you out

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°